Computing the minimum number of scalar multiplications needed to calculate the product of two matrices is a fundamental problem of algebraic complexity theory [1]}.
Since the pioneering work of Strassen [2]} we know that the complexity of computing the product of two matrices of the size \(N\times N\)  is at most
\(O(N^{2.81})\) . This asymptotic bound was improved several times, most recently by Coppersmith and Winograd [3]}, Williams [4]}, Le Gall [5]}, and Alman and Williams [6]}. The current best asymptotic complexity is \(O(N^{2.37286})\) .
